Question

A kilometre is very nearly equal to $.62138miles$; shew that the fractions $\frac{5}{8},\frac{18}{29},\frac{23}{37},\frac{64}{103}$ are successive approximations to the ratio of a kilometre to a mile.

Answer 1

Given,

1 kilometer = 0.62138 miles

$\frac{5}{8}=0.625\approx 0.62138$

$\frac{18}{29}=0.6206\approx 0.62138$

$\frac{23}{37}=0.6216\approx 0.62138$

$\frac{64}{103}=0.6213\approx 0.62138$

Hence proved.